Intrinsic symmetry of Ampère’s circuital law and other educational issues
Bibliographic record
Abstract
This paper explores Ampère’s circuital law (ACL) from an educational perspective. The interchangeability of the ampèrian loop with the current loop, an intrinsic symmetry of ACL that is seldom addressed in the literature or textbooks, is illustrated here. It is verified that the symmetry axis of a circular current is an ampèrian loop. The attempt to apply ACL to a finite wire, a common source of student misunderstanding, is used to highlight the limitations of ACL. The generalisation of ACL is illustrated using an instructive example where the displacement current is unconfined and not spatially uniform. This work is primarily intended for teachers and more advanced undergraduate students, who may benefit from the ideas that are presented here.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.011 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".